Projective Splitting with Forward Steps only Requires Continuity
This is an incremental improvement for researchers in optimization, making projective splitting algorithms more broadly applicable.
The paper tackled the problem of relaxing the Lipschitz continuity requirement in projective splitting algorithms for monotone operator inclusions, showing that a backtracking linesearch enables convergence with merely continuous operators in finite-dimensional spaces.
A recent innovation in projective splitting algorithms for monotone operator inclusions has been the development of a procedure using two forward steps instead of the customary proximal steps for operators that are Lipschitz continuous. This paper shows that the Lipschitz assumption is unnecessary when the forward steps are performed in finite-dimensional spaces: a backtracking linesearch yields a convergent algorithm for operators that are merely continuous with full domain.